Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include<cstdio>
#include<algorithm>
using namespace std;
int main()
{
  int n,i,A,B,C,D;
  int X,Y,Z,W;
  int a[1001];
  int min=100000001;
  double ans;
  scanf("%d",&n);
  for(i=0;i<n;++i) scanf("%d",&a[i]);
  sort(a,a+n);
  A = a[n-1];
  B = a[n-2];
  for(i=0;i<n-2;++i){
    if(a[i+1]-a[i]<min){
      min=a[i+1]-a[i];
      C = a[i+1];
      D = a[i];
    }
  }
  
  ans = (double)(A+B)/(C-D);

  if(a[n-1]-a[n-2]<min){
    X = a[n-3];
    Y = a[n-4];
    Z = a[n-1];
    W = a[n-2];
    ans = (ans>(double)(X+Y)/(Z-W)) ? ans : (double)(X+Y)/(Z-W);
  }
  
  
  printf("%f\n",ans);
}